Mathematics

Problem

The function

f:\mathbb{R}\to\mathbb{R}

is defined by

f(x)=|x-3|+2

. a. (i) Evaluate

f(7)

and

f(1)

. b. (ii) Rewrite

f(t)

without the modulus sign separately for the cases

t>3

and

t<3

. c. (iii) Using your expression from part (ii), find

f(3-k)

when

k>0